What happens if my rider doesn't start? Will I get my bet back?

tl;dr Betting houses have all the power and it's up to them.

Recently, Hugo Houle didn't start because they were sick. I had an E/W bet on them that I checked later in the day and it was marked as a loss instead of being voided. You have the ability to request that the bet be voided because the rider didn't start but it's up to the betting house in the end, and dealing with their (almost non-existing) customer support is probably not worth the price.

Cycling is a pretty niche sport, and an even niche-r betting market and the betting house doesn't always do the due diligence of who didn't finish because they were sick or because say, they got a mechanical. For the larger races, like Milan San Remo or Tour of Flanders they're usually on top of voiding DNS's, but that's not always the case.

Betting has inherent risk and unfortunately, it's par for the course you'll lose the bet in most cases.